The scattering of electromagnetic waves in fractal media

Abstract

The scattering of electromagnetic waves in fractal media is studied. The fractal dimension is naturally involved in the formulation of two physical problems studied in this paper. The general theory of multiple scattering of electromagnetic wave in fractal media is developed by modifying Twersky's theory. Statistical quantities, such as the average field and average intensity of the multiple scattered wave, are studied for a wave propagating in a fractal medium. The scattering cross section of the medium is deduced. The backscattering of electromagnetic waves is also studied. The results showing the range of dependence of the backscattered signals are in agreement with numerical simulations by Rastogi and Scheucher (1990). It also suggests a method of measuring the fractal dimension of the fractal embedded media using radar sounding. The theory developed in this paper can also be used for problems related to multiple scattering of other kinds of waves, such as acoustic waves, elastic waves etc, in fractal media.     

On the theory of the acceleration of plasma electrons during stimulated scattering of an intense laser wave

The mechanism of electron acceleration in the stimulated Raman forward scattering of a monochromatic laser wave in a cold plasma is investigated theoretically. It is shown that as a result of the stochastic interaction of the electrons with the ponderomotive wave and with plasma waves excited in the scattering process, some of the electrons are accelerated to relativistic energies. Zh. Tekh. Fiz. 69, 3–8 (January 1999)     

Applications of stimulated Raman scattering

The applications of stimulated Raman scattering reviewed in this paper include: determination of spontaneous Raman parameters and nonlinear susceptibilities by gain measurements and coherent anti-Stokes Raman spectroscopy, excitation of molecular vibrations and lattice waves and measurement of their relaxation times, generation of intense tunable light in the infrared region of the spectrum. The main results of the theory of stimulated Raman scattering relevant to the understanding of these applications are discussed.     

Multiphoton stimulated compton scattering

The processes of multiphoton Compton scattering of relativistic electrons are considered in a special one-dimensional geometry. The multiphoton parameter and the energy distribution of scattered electrons are found. The nonlinear behaviour of the gains of the two external electromagnetic waves is investigated in the saturation region. The multiphoton parameter is shown to be of order of one and the perturbation theory is shown to be inapplicable at very weak fields. For saturation of the gains much stronger fields are required which however are much weaker than those which are necessary for appearance of multiphoton processes in the spontaneous Compton scattering.     

Post-solitons and electron vortices generated by femtosecond intense laser interacting with uniform near-critical-density plasmas

Generation of nonlinear structures, such as stimulated Raman side scattering waves, post-solitons and electron vortices, during ultra-short intense laser pulse transportation in near-critical-density (NCD) plasmas is studied by using multi-dimensional particle-in-cell (PIC) simulations. In two-dimensional geometries, both P- and S-polarized laser pulses are used to drive these nonlinear structures and to check the polarization effects on them. In the S-polarized case, the scattered waves can be captured by surrounding plasmas leading to the generation of post-solitons, while the main pulse excites convective electric currents leading to the formation of electron vortices through Kelvin-Helmholtz instability (KHI). In the P-polarized case, the scattered waves dissipate their energy by heating surrounding plasmas. Electron vortices are excited due to the hosing instability of the drive laser. These polarization dependent physical processes are reproduced in two different planes perpendicular to the laser propagation direction in three-dimensional simulation with linearly polarized laser driver. The current work provides inspiration for future experiments of laser-NCD plasma interactions.     

Stimulated scattering of electromagnetic waves in a magnetised plasma

We present estimates of threshold powers, growth rates and amplification factors for stimulated scattering of electromagnetic waves off electrostatic modes in a magnetized plasma, The magnetic field strength is assumed to influence only the electrostatic modes and not the propagation of incident and scattered electromagnetic waves.     

Energy characteristics of photothermal vibrational instability at stimulated Raman and Mandelstam-Brillouin scattering in aerosol droplets

The threshold intensity and the combination frequencies for photothermal vibrational instability in high-Q aqueous aerosol droplets in the two-mode regime have been calculated. The selection rules for coupling electromagnetic and temperature modes in a droplet are obtained. A comparative analysis of the threshold excitation intensities of photothermal vibrational instability, stimulated Mandelstam-Brillouin scattering, and stimulated Raman scattering in droplets is performed. It is shown that photothermal vibrational instability in the two-mode regime can be developed at a pump intensity of about 10⁴ W/cm² for droplets with radii of 2–20 μm for a pump wavelength of 0.532 μm. A method of remote measurement of the microphysical droplet parameters from the additional periodic temperature shift of droplet eigenfrequencies in the spectrum of stimulated Raman scattering and lasing is proposed.     

Double stimulated mandelstam-brillouin scattering of electromagnetic waves of arbitrary polarization in an isotropic plasma

We study the nonlinear interaction of a system of incident and reflected electromagnetic waves of arbitrary polarization, propagating in a quasihomogeneous plane layer of isotropic plasma obliquely to the boundary, with scattered electromagnetic waves. These waves are coupled in the double stimulated Mandelstam-Brillouin scattering by a common sound wave that is parallel to the layer boundary. We examine the influence of the wave polarization on the threshold intensity, instability growth rate, and characteristics of the stationary solution. It is found that the nonlinear interaction scales are different for waves of different polarization. In particular, this leads to a change of the wave polarization in the course of the interaction. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 7, pp. 851–859, July, 1997.     

Stimulated resonance Raman scattering

A quantum mechanical theory of stimulated resonance Raman scattering taking full account of the effects of the incident and scattered radiation on the state and properties of the molecules is developed. The resulting formulas enable the amplification of the scattered radiation and the attenuation of the incident flux to be determined. The conditions under which stimulated Raman scattering produces amplification of radiation are formulated. The range of applicability of the theory, not taking account of the effects of radiation on the properties of the material is discussed.     

The scattering of electromagnetic waves in fractal media

The scattering of electromagnetic waves in fractal media is studied. The fractal dimension is naturally involved in the formulation of two physical problems studied in this paper. The general theory of multiple scattering of electromagnetic wave in fractal media is developed by modifying Twersky's theory. Statistical quantities, such as the average field and average intensity of the multiple scattered wave, are studied for a wave propagating in a fractal medium. The scattering cross section of the medium is deduced. The backscattering of electromagnetic waves is also studied. The results showing the range of dependence of the backscattered signals are in agreement with numerical simulations by Rastogi and Scheucher (1990). It also suggests a method of measuring the fractal dimension of the fractal embedded media using radar sounding. The theory developed in this paper can also be used for problems related to multiple scattering of other kinds of waves, such as acoustic waves, elastic waves etc, in fractal media.     

The effect of a local field on Raman scattering in a uniaxial crystal

This paper discusses the Raman scattering of light in an anisotropic crystal in the crystal optics approximation, taking into account local fields acting on the molecules. It shows that the effect of the local field reduces to the introduction of the effective Raman polarizability tensor of the molecules, which depends both on the properties of the molecules themselves and on the characteristics of the crystal at the frequencies of the incident and scattered waves. Raman scattering cross sections are obtained in a uniaxial crystal for various types of incident waves. It is shown that, in the case of an extraordinary incident wave, the local field substantially affects how the cross section depends on the direction of incidence. Zh. éksp. Teor. Fiz. 112, 180–191 (July 1997)     

X-ray scattering from a randomly rough surface

Abstract

On the basis of the method of reduced Rayleigh equations we present a simple and reciprocal theory of the coherent and incoherent scattering of x-rays from one- and two-dimensional randomly rough surfaces, that appears to be free from the limitations of earlier theories of such scattering based on the Born and distorted-wave Born approximations. In our approach, the reduced Rayleigh equation for the scattering amplitude(s) is solved perturbatively, with the small parameter of the theory η(ω) = 1 - ε(ω), where ε(ω) is the dielectric function of the scattering medium. The magnitude of η(ω) for x-rays is in the range from 10^?6 to 10^?3, depending on the wavelength of the x-rays. The contributions to the mean differential reflection coefficient from the coherent and incoherent components of the scattered x-rays are calculated through terms of second order in η(ω). The resulting expressions are valid to all orders in the surface profile function. The results for the incoherent scattering display a Yoneda peak when the scattering angle equals the critical angle for total internal reflection from the vacuum-scattering medium interface for a fixed angle of incidence, and when the angle of incidence equals the critical angle for total internal reflection for a fixed scattering angle. The approach used here may also be useful in theoretical studies of the scattering of electromagnetic waves from randomly rough dielectric-dielectric interfaces, when the difference between the dielectric constants on the two sides of the interface is small.     

Analysis of long wavelength electromagnetic scattering by a magnetized cold plasma prolate spheroid

Abstract

Using dielectric permittivity tensor of the magnetized prolate plasma, the scattering of long wavelength electromagnetic waves from the mentioned object is studied. The resonance frequency and differential scattering cross section for the backward scattered waves are presented. Consistency between the resonance frequency in this configuration and results obtained for spherical plasma are investigated. Finally, the effective factors on obtained results such as incident wave polarization, the frequency of the incident wave, the plasma frequency and the cyclotron frequency are analyzed.     

Theory of Raman light scattering by nanocrystal acoustic vibrations

A theory of Raman scattering of light by acoustic phonons in spherical nanocrystals of zinc-blende and wurtzite semiconductors has been developed with the inclusion of the complex structure of the valence band. The deformation-potential approximation was used to describe the exciton-phonon interaction. It is shown that this approximation allows only Raman scattering processes involving spheroidal acoustic phonons with a total angular momentum F=0 or 2. The effect of phonon quantum confinement on linewidth in Raman scattering spectra and scattered polarization is analyzed. An expression for the shape of the spectral line corresponding to nonresonant scattering from F=0 phonons was obtained. Fiz. Tverd. Tela (St. Petersburg) 41, 1473–1483 (August 1999)     

Imaging of random surfaces and inverse scattering in the Kirchoff approximation

Abstract

Imaging of random surfaces can be modelled by integration over angular spectra of scattered plane waves. This approach suggests the representation of surface scattering in the Kirchhoff approximation using the concept of three-dimensional spatial frequencies. Optical methods of surface profiling can thus be modelled, leading to an insight into reconstruction of surface profiles from scattering data. The methods can also be extended to cover thin-film multilayer structures.     

Large-amplitude plasma wave generation with a high-intensity short-pulse beat wave

A short-pulse laser beat wave scheme for advanced particle accelerator applications is examined. A short, intense (3-ps, >10(18)-W cm(-2)) two-frequency laser pulse is produced by use of a modified chirped-pulse amplification scheme and is shown to produce relativistic plasma waves during interactions with low-density plasmas. The generation of plasma waves was observed by measurement of forward Raman scattering. Resonance was found to occur at an electron density many times that expected, owing to ponderomotive displacement of plasma within the focal region.     

Angular scattering diagrams of linearly polarized relativistic-intensity electromagnetic radiation in a plasma

Instability of the propagation of nonlinear nonmonochromatic relativistic-intensity electromagnetic waves in a cold subcritical-density plasma is analyzed in three-dimensional geometry. Angular diagrams of their scattering are presented. The calculations show that forward and backward scattering may occur. The radiation in a specific direction is a set of harmonics, propagating against a continuum background, whose frequencies depend on the angle. Radiation at a specific frequency propagates in a set of scattering cones. The azimuthal cone angles depend on frequency. Zh. éksp. Teor. Fiz. 116, 1947–1962 (December 1999)     

A comparison of Raman scattering,resonance Raman scattering,and fluorescence from molecules adsorbed on silver island films

The enhancement of Raman scattering (RS), resonance Raman scattering (RRS), and fluorescence from molecules adsorbed on silver-island films is reported. A heirarchy of enhancements is found: 10⁵ for RS, 10³ for RRS, and 0.1–10 for fluorescence, depending on the quantum yield of the free molecule. Using the framework of the electromagnetic theory of surface-enhanced Raman scattering, generalized to treat molecular resonance phenomena, we develop a unified picture of the role of the surface plasmon resonances, and the surface-induced damping, in the light scattering processes. The observed heirarchy of enhancements is shown to have important spectroscopic consequences.